**2. Hybrid modeling procedure**

*Research Trends and Challenges in Smart Grids*

reasons, modeling of battery-packs is a difficult task.

information regarding the transient behavior of battery [10, 14].

The accuracy of a battery model depends on the procedure used to obtain its parameters. Modeling techniques can be classified from simple black-box approaches to time- or frequency-domain procedures. Black-box models are simple to obtain, but do not provide information on the battery's internal behavior. Time-domain models are obtained from the analysis of the battery voltage evolution during charge–discharge tests by means of the procedure called current interruption test. In order to improve the model accuracy, some authors [15, 16] use online parameter identification methods to predict battery dynamical behavior as a function of time. These models are relatively easy to obtain, but their validity is usually limited to specific load regimes [17]. Frequency-domain based models are performed by means of electrochemical impedance spectroscopy (EIS) tests [18, 19]. In this technique, a small AC excitation signal (either current or voltage) is applied as a variable frequency sweep to the battery. To obtain a linear model, the amplitude of the AC excitation signal applied to the cell is kept between 5 and 10% of the rated voltage/current. Although EIS models can be time-consuming to obtain, they can reproduce accurate battery behavior in a wide frequency range, typically from mHz to kHz [20, 21]. The equivalent complex impedance is calculated as the quotient between the instantaneous values of voltage and current for

Li-ion battery-packs are modeled in the majority of the cases as an aggregation of individual cell models, neglecting the packaging effects of multicell devices, although some recent works have shown that considering the interactions between cells and BMS elements can improve the accuracy of the Li-ion battery-packs models [22, 23]. Also, most battery models do not consider that battery modules can work at different dynamic regimes due to internal electrochemical processes that affect their transient behavior. In highly dynamic applications such as electrical grid support or frequency control in microgrids, there are three time constants of special interest [24]. The first one corresponds to the fast processes with dynamic performance from millisecond to seconds, and it is related to safety control of the battery-pack. The second constant refers to the load regime, which produces different charging/discharging cycles of the battery-pack. Finally, ageing processes that

(produced by manufacturing processes and/or ageing processes) from limiting the whole pack performance [6]. Besides electrochemical behavior of Li-ion cells, the performance of the battery-pack is affected by the interactions between cells and BMS components. This configuration increases the nonlinear behavior of commercial battery devices compared with single cells. For all these aforementioned

Several battery models have been proposed in literature in order to facilitate their integration into different applications. The most detailed models include electrochemical- or physical-based models, which are able to accurately describe the chemical processes taking place inside battery cells [7, 8]. Despite their accuracy, these models are very complex to be implemented in a simulation tool, and the coupled nonlinear differential equations that compose the model require heavy computational work [9, 10]. In contrast with electrochemical models, electrical circuit models are not very complex, allow the simulation of the electrical response of the battery by using electrical elements (resistances, RC networks, ideal voltage sources, etc.), and can be easily incorporated in control strategies and simulation platforms. The simplest electrical circuit model of a battery is given by Thevenin's equivalent circuit, which is composed of an ideal voltage source in series with a constant internal resistance [11–13]. This model can be used in an initial stage of battery dimensioning, but in the case of dynamic applications, it does not offer

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each test point.

To reproduce the behavior of Li-ion batteries using an electric circuit, the circuit topology includes a voltage source that represents the active behavior of the battery and a series impedance of the passive one. In the hybrid experimental procedure proposed in this work, the parameters of the electrical model have been calculated from experimental results of both time- and frequency-domain tests.

The modeling procedure is applied to a commercial battery-pack composed of four parallel-connected strings (seven cells connected in series in each string) and a battery management system. BMS functions include measurement of cell voltage, temperature, and current of each series connection, an algorithm for cell voltage balancing, and the disconnection during charging and discharge processes (to avoid cells over/under voltage). **Figure 1** shows a battery-pack connection scheme. The technical data of the battery-pack are presented in **Table 1**.

**Figure 1.** *Battery-pack connections.*


#### **Table 1.**

*Battery-pack technical data.*
